Morals don't need religion or God to form. Case in point come in the world of driving, there are many many rules listed in the highway code, lots of ways to signal and to indicate etc.
That's all very well, but a new driving morality has emerged on the roads not written down or even taught by driving instructors, it's driving manners. We as drivers learn soon enough that flashing your headlights is an invitation to let you out, flashing your emergency lights once is a 'thank you' to the car behind, beeping your horn shows dissatisfaction with another driver. We know that driving at less than the speed limit for no reason is 'bad driving' and we know that putting 'baby on board' signs in the car is a clear sign you're a dangerous driver. And we feel bad if we violate those rules.
These little rules and manners evolved naturally amongst the drivers themselves, not from a higher force carving them on tablets of stone, now if relatively complicated 'morals' can be developed amongst a community in less than a century(ish), you would expect rules like 'don't kill' and 'don't steal' to form in 10,000(ish) years